|1 + 2x| = 3x - 6.

Note that:

1. |1 + 2x| = 1 + 2x when 1 + 2x > 0 => x > -1/2.

2. |1 + 2x| = -(1 + 2x) = -1 - 2x when 1 + 2x < 0 => x < -1/2.

1. 1 + 2x = 3x - 6 AND x > -1/2 => x = 7 AND x > -1/2 => x = 7.

2. -1 - 2x = 3x - 6 AND x < -1/2 => x = 1 AND x < -1/2 => no solution.

So x = 7 is the only solution.